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SRB measures for certain Markov processes
We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then, when all the constituent maps have common fixed points at 0 and 1, theorems are given to analyze properties of the ergodic invariant measures \delta_0 and \delta_1. In particular, sufficient conditions for \delta_0 and/or \delta_1 to be, or not to be, SRB measures are given. We apply some of our results to asset market games.
History
School
- Science
Department
- Mathematical Sciences
Published in
Discrete and Continuous Dynamical Systems. Series AVolume
30Issue
1Pages
17 - 37 (21)Citation
BAHSOUN, W. and GORA, P., 2011. SRB measures for certain Markov processes. Discrete and Continuous Dynamical Systems. Series A, 30 (1), pp.17-37.Publisher
© American Institute of Mathematical SciencesVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2011Notes
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems, Series A following peer review. The definitive publisher-authenticated version, BAHSOUN, W. and GORA, P., 2011. SRB measures for certain Markov processes. Discrete and Continuous Dynamical Systems. Series A, 30 (1), pp.17-37, is available online at: https://doi.org/10.3934/dcds.2011.30.17.ISSN
1078-0947eISSN
1553-5231Publisher version
Language
- en
